Issue Description

Build compilation fails due to missing function definitions in the health check module.

Current Status

• Priority: High
• Estimated Time: 1 hour
• Impact: Affects health monitoring and deployment readiness

Error Details

cmd/github-mcp-server/health.go:119:28: undefined: claudeCheckcmd/github-mcp-server/health.go:127:28: undefined: githubCheck

Required Actions

1. Implement missingclaudeCheck function for Claude API connectivity validation
2. Implement missinggithubCheck function for GitHub API connectivity validation
3. Ensure health check endpoints return proper status codes
4. Test health check functionality in Docker containers

Acceptance Criteria

• Build compiles successfully without errors
• Health check endpoint responds with proper status
• Claude API connectivity validation works
• GitHub API connectivity validation works
• Health checks integrate properly with container orchestration

Related Files

• cmd/github-mcp-server/health.go
• docker-compose.yml (health check configuration)
• k8s/deployment.yaml (liveness/readiness probes)

Context

This issue was identified during final validation testing for the Claude auto-commit feature. The health check functionality is critical for production deployment monitoring.